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On the Collatz Conjecture

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  • Yao Moïse Blewoussi

Abstract

The Collatz conjecture (or Syracuse conjecture) states- all Syracuse sequences converge to 1. We present a Syracuse sequence, and we prove that the conjecture is true, first by using the fact that all convergent integer sequences are eventually constant. We then prove wrong 2 hypotheses- the case where the sequence tends to infinity, and the case where the sequence has no limit and is eventually periodic. We conclude by elimination, afterward.

Suggested Citation

  • Yao Moïse Blewoussi, 2024. "On the Collatz Conjecture," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(6), pages 1-28, December.
    • Handle: RePEc:ibn:jmrjnl:v:14:y:2024:i:6:p:28
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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